If the front and back of the ship are not accelerating at (at least very nearly) the same rate, you are tearing your ship apart.

I had replied (with a reference) in post 13.Essentially, if the two ends accelerate at the same rate (same g force applied for the same duration as measured by a local clock), then they'll stay the same distance apart (in the original frame) but the ship breaks up due to length contraction in that original frame.

The same thing can be expressed using accelerating frames, but that's the simplest explanation.

I have a ship that is a light year long. In frame P (parked) it extends from 0 (tail) to 366 (nose) light days.Now I accelerate it (or at least the tail) to .866c (dilation 50%) in one month as measured by a P clock....You can accelerate as hard as you like. There seems to be no limit.

I thought about this some more and found it unrealistic to accelerate the tail. The pilot is going to want to sit right in the middle where his commands can be carried out in minimal time. So how fast can the middle be accelerated? If the front accelerates less, the rear must accelerate harder. So is there a limit to that?I think not again, but it gets funny. My ship is two light years long (1 each way from our observer midpoint). I accelerate the pilot to .866c in a month, meaning the tail has to move .54 light years in a month, sort of. The sort of saves us, but since the clock at the tail moves backwards, does it need to reach into a time when the ship was stationary?

oops.Sorry, I missed that.But the problem is that, as I sit on the ship, there's nothing causing it to break. Any hypothetical breakage is at odds with causality.So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).

Good reading, yes. Haven't even got into it yet, but it opens with a discussion of fishing from a black hole, and equating that to an accelerating observer trailing something behind, exactly what I brought up in my prior post.

Without reading the article beyond that, I see a problem: This is equivalent to a uniform gravitational field of the same force as my acceleration at the ships midpoint. As I go further back, I'm getting deeper in the gravity well, until the escape velocity back there is light speed, and my ship cannot accelerate without breaking.

That means that a sufficiently long ship cannot accelerate at all. The tail can accelerate, but any arbitrary point above that has a limit, which is near zero for most of the ship.

But the problem is that, as I sit on the ship, there's nothing causing it to break. Any hypothetical breakage is at odds with causality.

Sure there is. Picture it as a series of ships, all accelerating identically and independently. As length contracts in the original frame, the separation between ships does not. So it breaks because gaps form. The ship becomes stretched, and it cannot take that.That's what the other thread was about, but it is framed as sort of a push for evidence of aether, which it isn't.

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So I know that the acceleration of the two ends are the same (and the clocks , which are stationary from my PoV, run at the same rate).

Yes, so the separation between the two clocks is always the same, but the ship length is not, so it breaks.

OK, Let's imagine there are a string of ships- each a foot apart, and each pilot carefully keeps a foot long ruler between his ship and the next.As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.So the rulers all still fit exactly into the gaps.

OK, Let's imagine there are a string of ships- each a foot apart, and each pilot carefully keeps a foot long ruler between his ship and the next.As the string all speed up all the rulers shorten. All the ships shorten and all the gaps between the ships shorten And they all shrink to exactly the same extent.So the rulers all still fit exactly into the gaps.

No, the gaps do not shorten, else the ship 20 light years ahead would be closer to the rear (in the frame where everyone was stopped) than before he started accelerating.Really, read the other thread. It totally discusses exactly that issue.

does not work.There needs to be something that I, on my ship, can see causing the break, or it won't happen.

Well, if they're a stack of independent ships, you see the gap widen. If it is one brittle object, you see it break due to being stretched. The forces of contraction don't bring the two pieces together like they would do on a real ship of reasonable length because there is an equal force the other way of the next ship pulling the opposite direction. The tension forces might alter the front and back a bit beyond what the engines are doing, but the middle has no choice but to break up.

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From my PoV, the ship stays the same length.

If the line of independent ships all behave the same, then from your POV (not on any of them), the line stays the same length, yes. But it is one object, and object contract with the speed it has from your POV, so it cannot stay the same length like the line of independent ships is trying to do.

No, the gaps do not shorten, else the ship 20 light years ahead would be closer to the rear (in the frame where everyone was stopped) than before he started accelerating.

Well, yes, and no.They don't shorten from my PoV- and that's exactly why my ship doesn't fall apart. If I use my (accelerating) ruler to measure the (equally accelerating) gap, I get the same measurement. From my PoV nothing is shrinking on my ship. The people I left behind at the launch pad are shrinking.

The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length.

Ok so you have a ship 1 light-year long moving with inertial motion. As the front passes you the rear sends a light signal towards you. If it takes less than 1 year to reach you then you can say that length contraction is physical. If it takes 1 year then length contraction is only a function of time dilation. An interesting proposition.

EDIT Of course then you have the issue of determining time dilation. Who do you consider to be moving and who is stationary?

Clocks forward of a given observer will appear to run faster, and clock behind a given observer will appear to run slower.

No, because you have stipulated that they are all accelerating at the same rate. You can't have your cake and eat it!

The key word here is "relativity". Every observation is made relative to what?

For one, the different parts of the ship are not accelerating at the same rate, else the ship would break apart. I stipulated that the ship was always stationary in the frame of any point in the ship at any time. There is a term for it that I learned from Janus's link: The ship is 'Born rigid'. Those frames are all different depending on the point in the ship. Anyway, this is needed for the ship to not break apart.

Secondly, perhaps I was not clear. My observer above is on the ship, not in any inertial frame. For such an observer, clocks (accelerating with the observer or not) ahead of the observer in the accelerating reference frame will advance at a pace greater than the observers clock, and clocks behind will lose time, even to the point of running backwards.

This is apparent in the Andromeda paradox where a calendar there might be October in my frame when the Earth spins me towards some planet in Andromeda, but is July there 10 hours later after I've accelerated away from it. Their clock has run backwards from my POV.That can't happen on my ship. If it did, the ship would break up.

You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there), and they take longer to do the same acceleration (the clocks run faster up there if you compare them to the lower floors). So that's why the ship holds together. The different parts are accelerating at different rates, just like the building.

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The gaps do shorten from someone else's perspective. But those people don't see anything fall apart, they just see the ship shrink slightly along its length.

This leads to a direct contradiction. From the perspective (in the frame F) of a stationary observer as the ships depart, ship X and Y both accelerate independently and identically. They are 10 light years apart, at location 0 (X) and 10 (Y), accelerating in the positive direction. They take 1 year to get to .866c relative to F so the ships are both now half their original length. Ship X has moved from 0 to about 0.45, and you say the gap of 10 light years has shortened to 5 light years, so Y is now at location 5.45, a location it could not reach from location 10 in just 1 year. It seems to have moved backwards at 4.5c despite accelerating forwards just like X did.

You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there),

It is very plainly different.

I can measure the gravitational field as I go up + down building, and I can work out from those reading how big the planet is.That measurement- the radius of the planet- gives me a "scale" for the rate of change of acceleration with distance.

But on a ship, in space there's no planet nearby.So there's nothing to calculate the change of acceleration with distance.

So there is no such change.

Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.That's a breach of causation.

OK, so we're considering a different frame F than the ship's frame S. Is the ship a light year of proper length (in S), or 1 light year long in the F? Given context of the question, you apparently assume a one light year proper length, and it is contracted in F. Just making sure. Our observer is O who is stationary in F.

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As the front passes you the rear sends a light signal towards you.

This is vague since no frame is specified. Let's call the event of the front passing the observer E1.I have one signal sent from the rear at an event E2 simultaneous with the E1 in frame F. Another signal is sent at event E3 which is simultaneous with E1 in frame S.

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If it takes less than 1 year to reach you then you can say that length contraction is physical. If it takes 1 year then length contraction is only a function of time dilation. An interesting proposition.

O will measure less than a year between E1 and getting the signal from E2 or E3, but the E2 signal gets to him first.

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EDIT Of course then you have the issue of determining time dilation. Who do you consider to be moving and who is stationary?

You ship is no different from a building sitting on a planet with a gravitational field identical to the acceleration of the ship. The upper floors accelerate less (you can tell because you weigh less up there),

It is very plainly different.

Einstein says they're identical, except that the building would need to be in a uniform gravitational field, and Earth's field is uniform only over limited heights. The exact analogy would be a building in a perfect uniform field.

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I can measure the gravitational field as I go up + down building, and I can work out from those reading how big the planet is.

No you cannot. You need more information than that to measure radius. There are 4 planets with gravity pretty much the same as Earth, so the guy measuring his weight change would not know the very different radius of the different planets. Saturn is actually the closest gravity to Earth.

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But on a ship, in space there's no planet nearby.So there's nothing to calculate the change of acceleration with distance.

You can walk up and down the ship with a scale, just like you did with the building.

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Fundamentally, you are saying that my ship falls apart as I watch , but no matter how hard I look on my ship, I can find no source of the force that causes it to break up.

The force is the front of the ship pulling too hard, trying to get further ahead of the rear.

Please comment on the contradiction I pointed out in my prior reply to you.

OK, so we have an acceleration limit on our long object.So let's give an example, and see if we can generalize afterwards.

I have a ship that cannot take stress as I've described. It is 100 light years in length, stopped in Frame F. I want to move it forward by one light hour (about 1.08 billion km) in frame F. How quickly (as measured in F) can I do that? Obviously a tiny object can do it in about an hour at maximum speed.

We can't go at maximum speed. If the tail T accelerates to c in an instant, the nose N requires 100 years to get up to that speed and by that time it has moved far further than a lousy light hour. So it seems we want to instantly accelerate T just enough to get the nose of the ship to our destination (100 LY + 1 light hour) in the frame of T, and then instantly accelerate N by the opposite amount to drag the tail up the same distance. Boom. We've moved the desired distance.

So let's see, there are 876000 hours in a century, so we want to dilate the distance between the target of N and the current position of T by that factor (876000/875999) which happens at about 452 km/sec. So I instantly accelerate T to 452 km/sec, and then slow down at a steady pace until I stop. That's an average of 226 km/sec, so it takes over 55.3 days to move my ship that far. It cannot be done faster. Passengers near either end will die of the G forces if the engines don't accelerate them with the rest of the fragile ship, but the ones in the middle will experience a snail-like acceleration of about 0.68 m/sec every hour.I will get disagreements of course, but I'm going to defend that answer.

The force is the front of the ship pulling too hard, trying to get further ahead of the rear.

No.I carefully set the engines to produce the same acceleration.Each section of the ship has the same mass.So, they all are subject to the same forces.All that force (for each section) goes into moving that bit of the shipSo there's none left over to pull my ship apart.